High-Speed Multi-Dimensional Beam Scanning System With Angle Amplification

ABSTRACT

A beam-steering system having high positional resolution and fast switching speed is disclosed. Embodiments of the beam-steering system comprise a diffraction limited optical system that includes a reflective imager and two controllably rotatable MEMS elements. The optical system is characterized by a folded optical path, wherein light propagating on the path is incident on each MEMS element more than once. Each MEMS element imparts an optical effect, such as angular change, on the output beam. By virtue of the fact that the optical system is multi-bounce optical system, the optical effect at each MEMS element is multiplied by the number of times the light hits that MEMS element.

STATEMENT OF RELATED CASES

This application claims priority of provisional patent application U.S.Ser. No. 60/990,506, filed 27 Nov. 2007 (Attorney Docket:RWF-01579-1240), the entire contents of which are herein incorporated byreference.

STATEMENT REGARDING FEDERALLY-SPONSORED RESEARCH

This invention was made with Government support under contractCCF-0520702, awarded by the National Science Foundation. The Governmenthas certain rights in the invention.

FIELD OF THE INVENTION

The present invention relates to beam-steering in general, and, moreparticularly, to two-dimensional beam-steering.

BACKGROUND OF THE INVENTION

There are applications in which it is desirable to direct a light beamto any point in a three-dimensional space. Often, the light beam must beswitched between two points with high speed. To satisfy this need,two-dimensional beam-steering systems based on rotating micromechanicalmirrors have been developed.

Micro-Electro-Mechanical Systems (MEMS) technology has been widelyapplied to optical beam-steering applications. MEMS devices are capableof switching speeds on the order of tens of kHz and are thereforewell-suited to optical applications that require switching times of afew hundred microseconds.

But there are applications, such as atomic-based quantum computing, thatrequire switching speeds on the order of 1 microsecond. In a quantumprocessor, a light beam is used to interrogate particles, referred to asqubits, which are located within a two-dimensional lattice. Qubits aretypically electrons, photons, or ions whose charge or polarization canbe changed by shining light of a particular wavelength on them. Thesequbits are typically separated from one another within the lattice byonly a few microns.

High-speed switching is particularly important in quantum processingbecause qubits must typically be addressed (illuminated) at frequenciesgreater than 1 MHz to keep them from randomly changing state. BecauseMEMS devices have been inadequate for this application, switchingdevices based on acousto-optical or electro-optical deflectors have beenused. Although they possess the requisite speed, these devices exhibitother drawbacks.

In particular, acousto-optical or electro-optical deflectors aredifficult to wavelength tune and are typically suitable for only asingle wavelength. Also, acousto-optical deflectors induce smallfrequency shifts in the laser that must be managed. These issues areproblematic because different qubits in the processing lattice willsometimes require different, specific wavelengths of light to effect aphase change. For example, a trapped ion might require ultraviolet light(of a specific wavelength), while a trapped neutral atom might requireinfrared light. In fact, a single qubit might require two differentwavelengths of light at the same time to cause a phase change.

Additional drawback are that acousto-optical deflectors are powerintensive and electro-optic deflectors require large operating voltageswhile providing only limited angular range.

A beam-steering system that is readily tunable and that is capable ofhigh speed switching with position resolution of a few microns wouldtherefore represent a significant advance in the state of the art.

SUMMARY OF THE INVENTION

The present invention enables steering of an optical beam without someof the costs and disadvantages of the prior art. Embodiments of thepresent invention provide a substantially diffraction-limited opticalsystem that enables switching of an optical beam between points in anarea with high speed. Embodiments of the invention are well-suited foruse in one- and two-dimensional beam-steering applications such asoptical switching in communications systems, data storage, laser-guidedweaponry, and displays, confocal microscopy, cell manipulation systems(e.g., optical tweezers, etc.), and imaging systems. Embodiments of thepresent invention are particularly well-suited for use in high-speedbeam-steering applications, such as quantum processing and quantumcomputing.

The illustrative embodiment of the present invention is atwo-dimensional beam-steering system that comprises a reflective imagerand two mirrors, each of which is controllably rotatable about a singlerotation axis. The imager and mirrors collectively define a foldedoptical path wherein a light beam is incident on each of the mirrorstwice. The rotation axes of the two mirrors are orthogonal to oneanother; therefore, the two mirrors can cooperatively steer an incidentbeam along any angle within a two-dimensional angular cone. By virtue ofthe fact that the light beam hits each mirror twice, rotation of amirror induces an angular change on the output beam that is at leasttwice the angular change induced by prior-art beam-steering systems. Asa result, for a given angular range of the output beam, a mirrorrequires half of the rotation range of a prior-art mirror. This reducedrotation range requirement provides the present invention advantagesover the prior art, such as faster response, lower polarization effects,and lower drive voltage.

In some embodiments, reflective elements are used in place of themirrors to enable the beam-steering system to induce other opticaleffects on the output beam. These optical effects include, withoutlimitation, wavefront modulation, aberration correction, spatialmodulation, phase modulation, chromatic filtering, polarizationfiltering, polarization rotation, and other polarization effects.

An embodiment of the present invention comprises: an optical system,wherein the optical system receives a first beam on a first input paththat is at a first input angle, θ_(In1), with respect to an opticalaxis, and wherein the optical system directs the first beam on a firstoutput path that is at a first output angle, θ_(Out1), with respect tothe optical axis, and further wherein the optical system comprises; afirst element whose angular position about a first rotation axis iscontrollable; a second element whose angular position about a secondrotation axis is controllable; and a reflective imager, wherein a changein the angular position of the first element about the first rotationaxis by Δφ1 results in a change in θ_(Out1) that is greater than|2xΔφ1|, and wherein a change in the angular position of the secondelement about the second rotation axis by Δφ2 results in a change inθ_(Out1) that is greater than |2xΔφ2|.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A depicts a schematic diagram of a portion of a quantuminformation processor in accordance with an illustrative embodiment ofthe present invention.

FIG. 1B depicts a schematic diagram of qubit array 114 in accordancewith an illustrative embodiment of the present invention.

FIG. 2A depicts conventional two-dimensional beam steering system 200based on transmissive optics.

FIG. 2B depicts a schematic diagram of details of a two-dimensionalbeam-steering system based on reflective optics.

FIG. 3A depicts a cross-sectional view of a conventional torsional MEMSmirror.

FIG. 3B depicts a top view of a conventional torsional MEMS mirror.

FIG. 4A depicts two-dimensional beam-steering system 104 in itsquiescent state in accordance with the illustrative embodiment of thepresent invention.

FIG. 4B depicts beam-steering system 104 in a first activated state inaccordance with the illustrative embodiment of the present invention.

FIG. 4C depicts beam-steering system 104 in a second activated state inaccordance with the illustrative embodiment of the present invention.

FIG. 5 depicts a method for controlling the direction of an output beamin two dimensions, in accordance with the illustrative embodiment of thepresent invention.

FIG. 6 depicts a schematic diagram of details of a one-dimensionalbeam-steering system in accordance with a first alternative embodimentof the present invention.

FIG. 7A depicts a schematic diagram of details of a two-dimensionalbeam-steering system in accordance with a second alternative embodimentof the present invention.

FIG. 7B depicts a schematic diagram of details of element array 706.

FIG. 8 depicts a method for independently controlling the direction ofeach of a plurality of output beam in two dimensions, in accordance withthe second alternative embodiment of the present invention.

FIG. 9A depicts a side view of a torsional MEMS element for inducing anoptical effect on output beam 106, in an unenergized state, inaccordance with a third alternative embodiment of the present invention.

FIG. 9B depicts a side view of a torsional MEMS element for inducing anoptical effect on output beam 106, in an energized state, in accordancewith the third alternative embodiment of the present invention.

DETAILED DESCRIPTION

The following terms are defined for use in this Specification, includingthe appended claims:

-   -   Orthogonal is defined as an orientation of at least two        elements, wherein the orientation composes only right angles,        whether in a single plane or in parallel planes. For example, a        first line in a first plane and a second line in a second plane        are considered orthogonal if the projection of the second line        onto the first plane is orthogonal with the first line in the        first plane.    -   Quiescent state is defined as a non-electrically activated        state. For example, a beam-steering system comprising        controllably rotatable elements is in its quiescent state when        its elements are unrotated from their as-fabricated positions.        Further, a controllably rotatable element is in its quiescent        state when its control voltages are equal to zero and it is        unrotated from its as-fabricated position.    -   Single-bounce optical system is defined as an optical system        that comprises a plurality of controllably rotatable elements,        wherein the optical path of the optical system is incident on        each controllably rotatable element once.    -   Multi-bounce optical system is defined as an optical system that        comprises a plurality of controllably rotatable elements,        wherein the optical path of the optical system is incident on        each controllably rotatable element more than once

FIG. 1A depicts a schematic diagram of a portion of a quantuminformation processor in accordance with an illustrative embodiment ofthe present invention. Processor 100 comprises input beam 102,beam-steering system 104, Fourier optics 110, telescope 112, and qubitarray 114. Input beam 102, beam-steering system 104, Fourier optics 110,and telescope 112 are substantially concentric along principle axis 116.

FIG. 1B depicts a schematic diagram of qubit array 114 in accordancewith an illustrative embodiment of the present invention. Qubit array114 comprises qubits 118-1,1 through 118-5,5 (collectively referred toas qubits 118). Qubits 118 are arranged in a 5×5 regular array having anarray spacing of approximately 8 microns in both the x-direction andy-direction. In some embodiments, a state change of one or more ofqubits 118 requires simultaneous excitation by multiple light beamshaving different wavelengths.

Beam-steering system 104, Fourier optics 110, and telescope 112collectively define a diffraction-limited optical system capable ofsteering light of input beam 102 to any qubit 118-i,j (where each of iand j is an integer within the range of 1 through 5) in qubit array 114.In order to access each of qubits 118, therefore, the optical systemmust be capable of rapidly directing output beam 106 to any point withinarea 120, which represents the cross-sectional area of two-dimensionalangle cone 108 at qubit array 114. It should be noted that the number ofelements in qubit array 114 is selected for exemplary purposes only andthat the present invention is applicable to qubit arrays having anynumber of elements.

Input beam 102 is a monochromatic light signal having a wavelengthsuitable for the excitation of atoms within qubit array 114. Thewavelength for input beam 102 is selected based upon the particular typeof atom to be excited. For example, in the illustrative embodiment,input beam 102 has a wavelength of 780 nanometer (nm), which is suitablefor exciting rubidium atoms. In some embodiments, input beam 102comprises multiple wavelengths. It will be clear to one skilled in theart, after reading this specification, how to specify, make, and usealternative embodiments of the present invention that operate at anydesired wavelength or wavelengths.

Beam-steering system 104 is an optical system that receives input beam102 and provides output beam 106. Input beam 102 is received at a fixedangle with respect to the optical axis of beam steering system 104.Output beam 106 is provided at any angle within the two-dimensionalangle cone 108. In FIG. 1A, output beam 106 is depicted as threedistinct output beams: (1) 106-0, coincident with and directed alongprinciple axis 116; (2) 106-1, directed along the extreme negative anglewithin the y-z plane; and (3) 106-2, directed along the extreme positiveangle within the y-z plane. Output beams 106-1 and 106-2 represent theextreme angles of output beam 106 within the y-z plane oftwo-dimensional angle cone 108, while beam 106-0 represents output beam106 when beam-steering system 104 is in its quiescent state. Thoseskilled in the art will understand that output beam 106 is alsocharacterized by output beams within the x-z plane, as well as acontinuum of angles in between the y-z and x-z planes; however, forclarity, these output beams are not depicted. Beam-steering system 104is described in more detail below and with respect to FIGS. 4A-C and 5.

Fourier optics 110 is an optics arrangement that receives output beam106 at an angle with respect to principle axis 116 and translates theangle of the received beam into a lateral shift from principle axis 116.In some embodiments, Fourier optics 110 includes a relay stage. In someembodiments, Fourier optics 110 includes a spatial filter.

Telescope 112 is a telescope imager for scaling the spatial distributionof output beams 106 from that provided by Fourier optics 110 to thespatial resolution of the qubits in qubit array 114.

In some embodiments, operation at more than one wavelength of light isdesirable. As a result, in some embodiments, the lenses included in eachof Fourier optics 110 and telescope 112 are suitable for low-aberrationoperation at multiple wavelengths.

Principle axis 116 represents the direction of propagation of input beam102 and output beam 106 when beam-steering system 104 is in itsquiescent state.

In operation, processor 100 steers output beam 106 by redirecting inputbeam 102 along an angle relative to principle axis 116. Fourier optics110 receives output beam 106 and provides it as a light beam thatpropagates along a direction substantially parallel to principle axis116. The angle of output beam 106, as received by Fourier optics 110, isconverted into a lateral shift from principle axis 116. Telescope 112receives output beam 106 and provides demagnification to match thespatial resolution necessary for interrogating individual qubits ofqubit array 114.

FIG. 2A depicts conventional two-dimensional beam steering system 200based on transmissive optics. Beam steering system 200 is discussed hereto provide background for the discussion of inventive beam steeringsystem 104.

Beam-steering system 200 comprises mirror 204, lens 210, and mirror 212.Mirrors 204 and 212 are rotatable mirrors that are reflective for inputbeam 200. Mirror 204 is controllably rotatable about rotation axis 206.Mirror 212 is controllably rotatable about rotation axis 214. By virtueof the fact that rotation axes 206 and 214 are orthogonal to oneanother, mirrors 204 and 212 cooperatively provide two-dimensionalbeam-steering.

Lens 210 is a conventional transmissive lens having a focal length of f.Mirrors 204 and 212 are located at a distance of 2×f from lens 210. As aresult, the surface of mirror 204 is substantially imaged onto thesurface of mirror 212.

In operation, mirror 204 receives input beam 202 and reflects it aslight beam 208. The path of light beam 208 within the y-z plane isdictated by the rotation angle of mirror 204 about rotation axis 206.Light beams 208-1 and 208-2 represent the extreme paths for light beam208 within the y-z plane. Light beam 208-0 represents the principle pathfor light beam 208 (i.e., the path for light beam 208 when mirror 204 isin its quiescent state).

Mirror 212 receives light beam 208 and reflects it as output beam 216.The path of output beam 216, into and out of the page as depicted inFIG. 2, is dictated by the rotation angle of mirror 212 about rotationaxis 214.

It will be apparent to one skilled in the art that a change in therotation angle of either of mirrors 204 and 212 about their respectiverotation axes will result in a change in the angle of output beam 216 byan amount equal to twice that rotation. As a result, a maximum desiredangular range for output beam 216, A_(Max), requires an maximum rotationrange, φ_(Max), for mirror 204, where φ_(Max)=φ_(Max)/2.

Although beam-steering system 200 is suitable for steering output beam216 in two-dimensions, it has several key disadvantages. First, theangles of incidence for input beam 202 at mirror 204 and light beam 208at mirror 212 are very high (approximately 45 degrees). This typicallyresults in polarization dependent operation. Second, even with amagnification by a factor of two, many applications require mirrors thathave a large angular range. This can be difficult to achieve for MEMSdevices, particularly if high-speed is also required. Third, refractivelenses typically exhibit chromatic dispersion, which makes operation atmultiple wavelengths difficult. Fourth, transmissive optical systems arelarge and notoriously difficult to align.

FIG. 2B depicts a schematic diagram of details of a two-dimensionalbeam-steering system based on reflective optics. Beam-steering system218 comprises mirror 204, mirror 212, and reflective imager 220.Beam-steering system 218 is an optical analog to beam-steering system200; however, beam-steering system 218 is provides a folded optical pathfor light beam 208.

Reflective imager 220 comprises a spherical mirror having an opticalaxis 222 and a focal length f1. In some embodiments reflective imager220 comprises an element other than a spherical mirror. Other elementssuitable for use in reflective imager 220 include spherical mirrors,elliptical mirrors, aspheric mirrors, or mirrors having complex surfacefunctions.

Mirrors 204 and 212 are substantially coplanar, wherein the reflectivesurface of each mirror aligns with plane P. Plane P is located at adistance of 2×f1 from reflective imager 220. Rotation axes 206 and 214are in an orthogonal relationship to one another; therefore, theycollectively enable two-dimensional beam-steering. Mirror 204 ischaracterized by mirror optical axis of 224, which intersects rotationaxis 206. Mirror 212 is characterized by mirror optical axis of 226,which intersects rotation axis 214. Mirror optical axes 224 and 226 aresubstantially parallel and coplanar with optical axis 222. Further,mirror optical axes 224 and 226 are at an equidistant distance c fromoptical axis 222.

Input beam 202 is received by mirror 204 at input angle θ_(In1). Mirror204 reflects input beam 202 as light beam 208 on path 230. Light beam208 is received by reflective imager 220 at optical axis 222 andreflected on path 232. Path 230 and 232 collectively define foldedoptical path 228. Light beam 208 is received by mirror 212 and reflectedas output beam 216 at angle θ_(Out1). When beam-steering system 218 isin its quiescent state, θ_(In1) and θ_(Out1) are equal.

FIGS. 3A and 3B depict cross-sectional and top views, respectively, of aconventional torsional MEMS mirror. Mirror 300 is discussed here toprovide background for the discussion of inventive beam steering system104. Mirror 300 is representative of elements 202 and 204.

Mirror 300 is a MEMS device that is controllably rotatable aboutrotation axis 318. Mirror 300 comprises plate 302, surface 304, tethers306, frame 308, spacer 310, substrate 312, and electrodes 314 and 316.

Typically, plate 302, tethers 306, and frame 308 are sculpted from asingle layer of structural material. Materials suitable for use as MEMSstructural material include, without limitation: single-crystalsemiconductors, such as silicon, gallium arsenide, germanium, siliconcarbide, and the like; polycrystalline semiconductors; ceramics; metals,polymers, and glasses.

Plate 302 is a structurally rigid circular region of structuralmaterial. Plate 302 commonly has a thickness within the range ofapproximately 300 nm to approximately 50 microns. Diameter, D, of plate302 is sufficient to reflect input beam 202 without inducing clipping.The thickness of plate 302 is suitable for supporting the formation of amirror in or on surface 304 such the resulting structure exhibitsnegligible curvature. For devices used in high-speed applications, it isdesirable to keep the thickness of plate 302 as thin as possible toreduce the moment of inertia of the mirror plate.

Tethers 306 are mechanically connected between plate 302 and frame 308.Tethers 306 are torsional springs that enable the rotation of plate 302about rotation axis 318. Tethers 306 define rotation axis 318, whichbisects the plate 302. As a result, the center of plate 302 remainssubstantially fixed in space when plate 302 rotates about rotation axis318. Tethers 306 provide a restoring force that returns plate 302 to itsquiescent position upon the removal of an actuation force. The shape andlength of tethers 306 are determined by the desired response time anddrive voltage for mirror 300. Conventional MEMS torsional springscomprise structural elements such as straight beam tethers, serpentinesprings, and the like.

It should be noted that for a typical MEMS element, the distance betweenrotation axis 318 and the plane of surface 304 is negligible.

In its quiescent state, plate 302 is separated from each of underlyingelectrodes 314 and 316 by an initial air gap g_(o).

In response to a drive voltage applied between electrode 314 and plate302, plate 302 rotates counter-clockwise about rotation axis 318. Inresponse to a drive voltage applied between electrode 316 and plate 302,plate 302 rotates clockwise about rotation axis 318. The appliedvoltages generate an electrostatic force on plate 302, the magnitude ofwhich is approximately inversely proportional to the square of theseparation between the electrode and mirror plate.

A change in the rotation angle of either of mirrors 204 and 212 abouttheir respective rotation axes will result in a change in the angle ofoutput beam 216 by an amount equal to twice that rotation angle. As aresult, an angular range of φ_(Max) of each of mirrors 204 and 212translates into an angular range of 2φ_(Max) for output beam 216 in thex-z plane and y-z plane, respectively.

Beam-steering system 218 has several advantages over beam-steeringsystem 200, by virtue of its folded optical path. First, the angle ofincidence for the light beams at the mirrors is reduced; therefore,polarization dependence is also reduced. Second, a reflective elementtypically has significantly less chromatic dispersion than atransmissive element. As a result, beam-steering system 218 can be lesswavelength sensitive than beam-steering system 200. Third, since theyare coplanar, mirrors 202 and 204 can be fabricated on a singlesubstrate. Finally, beam-steering system 218 is more compact thanbeam-steering system 200 and typically easier to align.

Unfortunately, beam-steering system 218 does not offer a significantadvantage over beam-steering system 200 with regard to maximum angularrange and response speed.

The design of a torsional MEMS mirror is a delicate balance within amulti-dimensional design space. It typically requires a trade-offbetween the maximum angular range, the speed at which the deviceresponds to a change in a control signal, the magnitude of the controlvoltage, and the size of the mirror.

The maximum rotation angle, φ_(Max), for plate 302 is substantiallydetermined by an electrostatic instability that occurs when theseparation between plate 302 and its driven electrode is reduced toapproximately ⅔ of initial gap g_(o). At this point, plate 302accelerates uncontrollably until it contacts the substrate. This iscommonly referred to as electrostatic “snap-down.”

Ways to increase φ_(Max) include reducing the diameter D of plate 302 orincreasing initial air gap g_(o). For most optical applications,however, the diameter, D, of plate 302 is determined by the requirementsof its optical system. Increasing g_(o) can be problematic since itresults in a higher required drive voltage for the device.

In many applications, including beam-steering for quantum processing,fast response time is a critical device parameter. Traditionally, fastresponse time has been achieved by sacrificing angular range.

In some prior art devices, an increased drive voltage has been used tomore rapidly drive a mirror to a desired rotation angle. Unfortunately,practical limitations on absolute voltage level, as well as voltage slewrate can limit the effectiveness of this approach. In addition,high-voltage electronics are typically expensive and less reliable thanconventional electronics.

The inventors recognized that a torsional element requires less time tomove a smaller distance. As a result, response time can be improved bylimiting the range of motion of a torsional element. At the opticalsystem level, therefore, the response time for beam steering system 218can be improved by reducing the magnitude of the angular change of itstorsional mirrors necessary to induce a desired change in the outputangle of an output beam from the system. The present inventionaccomplishes this through a change in the optical system that magnifiesthe effect of each mirror's rotation angle on the angle on the directionof the output beam. This obviates the need to increase the maximumangular range of the mirror itself. As a result, some or all of thedisadvantages discussed above can be mitigated or eliminated.

FIG. 4A depicts two-dimensional beam-steering system 104 in itsquiescent state in accordance with the illustrative embodiment of thepresent invention. System 104 comprises element 402, element 404,reflective imager 406 and bulk turning mirrors 432 and 434. System 104receives input beam 102 along principle axis 116 and provides outputbeam 106 along output angle, φ_(Out2), with respect to principle axis116. Output angle, φ_(Out2) is any desired angle within two-dimensionalangular cone 108. System 104 is a multi-bounce optical system, where thenumber of bounces per element, n, is equal to 2.

FIG. 5 depicts a method for controlling the direction of an output beamin two dimensions, in accordance with the illustrative embodiment of thepresent invention. Method 500 begins with operation 501, whereintwo-dimensional beam-steering system 104 (hereafter referred to assystem 104) is provided. Method 500 is described with continuingreference to FIGS. 1 and 4A-C. Method 500 begins with operation 501,wherein system 104 is provided.

Elements 402 and 404 are single-axis torsional MEMS mirrors. In theillustrative embodiment, each of elements 402 and 404 is analogous toelement 300, described above and with respect to FIGS. 3A and 3B.

Although elements 402 and 404 are planar-electrode-driven MEMS devices,it will be clear to one skilled in the art, after reading thisspecification, how to make and use alternative embodiments of thepresent invention that comprise:

i. torsional devices that comprise vertical comb-drive actuators; or

-   -   ii. nano-electro-mechanical devices; or    -   iii. macro-scale devices; or    -   iv. thermally actuated devices; or    -   v. microfluidically actuated devices; or    -   vi. magnetically actuated devices; or    -   vii. piezoelectric actuators; or    -   viii. any combination of i, ii, iii, iv, v, vi, and vii.

Each of elements 402 and 404 comprises a mirror surface that issubstantially reflective for input beam 102. In some embodiments, one orboth of elements 402 and 404 comprises a surface that comprises one ormore of an adaptive optic element, deformable mirror, spatial filter,phase modulator, spatial light modulator, shutter, chromatic filter,polarization filter, polarization phase filter, polarizer, and the like.

Element 402 is controllably rotatable about rotation axis 408 to anyangle within its maximum angular range. Rotation axis 408 is alignedwith the y-direction, as shown. Element 402 is characterized by mirroroptical axis 410, which is centered on the reflective surface of element402. Mirror optical axis 410 and rotation axis 408 intersect at thecenter of element 402.

In similar fashion, element 404 is controllably rotatable about rotationaxis 412 to any angle within its maximum angular range. Rotation axis412 is aligned with the x-direction, as shown. Element 404 ischaracterized by mirror optical axis 414, which is centered on thereflective surface of element 404. Mirror optical axis 414 and rotationaxis 412 intersect at the center of element 404.

Reflective imager 406 comprises a spherical mirror that is substantiallyreflective for light signal 102. In the illustrative embodiment,reflective imager 406 is analogous to reflective imager 220, describedabove and with respect to FIG. 2B. Reflective imager 406 ischaracterized by focal length f1 and optical axis 416. In someembodiments, optical axis 416 and principle axis 116 are substantiallyorthogonal. Although the illustrative embodiment comprises a reflectiveimager that comprises a spherical mirror, it will be clear to oneskilled in the art, after reading this specification, how to specify,make, and use a reflective imager that is an aspherical mirror, anelliptical mirror, or a mirror having a complex surface function.

Elements 402 and 404 and reflective imager 406 are arranged such thatelements 402 and 404 are coplanar with plane P, which is located at adistance substantially equal to twice the focal distance of reflectiveimager 406 (i.e., 2f1). Plane P and optical axis 416 are substantiallyorthogonal. Further, elements 402 and 404 are arranged symmetricallyabout optical axis 416 such that mirror optical axes 410 and 414 areequidistant from and substantially coplanar with optical axis 416. Whensystem 104 is in its quiescent state, the reflective surfaces ofelements 402 and 404 are coplanar with plane P and the rotation anglesof elements 402 and 404 about their respective rotation axes are zero.As a result, when system 104 is in its quiescent state, the optical pathbetween input beam 102 and output beam 106 is symmetrically folded aboutoptical axis 416 and θ_(Out2) and θ_(In1) are substantially equal.

Rotation axis 408 and rotation axis 412 are oriented orthogonally withrespect to one another. As a result elements 402 and 404 and reflectiveimager 406 are collectively capable of steering output beam 106 alongany direction within two-dimensional cone 108. In some embodiments,two-dimensional beam-steering is provided by a single MEMS device thatis capable of rotation about two axes. It should be noted, however, thatthe use of a pair of single-axis torsional elements to providetwo-dimensional beam steering can enable faster system performance.

The arrangement of reflective imager 406 and elements 402 and 404 isanalogous to the arrangement of elements 204 and 212 of beam-steeringsystem 218. As a result, for an input beam received at angle θ_(In1),with respect to optical axis 416, system 104 represents a single-bouncesystem.

Bulk turning mirror 432 is a bulk mirror that is oriented at a fixedangle with respect to principle axis 116. Bulk mirror 432 is orientedsuch that it receives input beam 102 and redirects it to element 402 atfixed input angle, θ_(In2), with respect to optical axis 416,

Bulk turning mirror 434 is a bulk mirror that is oriented at a fixedangle with respect to principle axis 116 and optical axis 416. Bulkmirror 434 is oriented such that it directs output beam 106 alongprinciple axis 116 when system 104 is in its quiescent state.

At operation 502, the value of θ_(In2) is selected to be substantiallyequal to 3θ_(In1).

At operation 503, input beam 102 is received at system 104. Input beam102 is substantially focused onto element 402 such that input beam 102has beam waist suitable to minimize loss of light due to clipping of thebeam by element 402. Input beam 102 is received at angle θ_(In2), withrespect to optical axis 416. Input beam 102 is reflected by element 402as light beam 428 on optical path 430. By virtue of the value ofθ_(In2), optical path 430 hits each of elements 402 and 412 twice.System 104, therefore, is characterized as a multi-bounce system,wherein n=2.

At operation 504, output beam 106 is provided from system 104. Outputbeam 106 is provided at angle θ_(Out2), with respect to optical axis416.

At operation 505, a control voltage is applied to element 402 to controlits rotation angle about rotation axis 408. As a result, this controlvoltage also controls the angle of output beam 106 in the x-z plane.

At operation 506, a control voltage is applied to element 404 to controlits rotation angle about rotation axis 412. As a result, this controlvoltage also controls the angle of output beam 106 in the y-z plane.

Operations 505 and 506 collectively control the direction of output beam106 along any angle within two-dimensional angle cone 108. As a result,operations 505 and 506 collectively enable output beam 106 to accesspoint within area 120 and, therefore, any qubit 118-i,j within qubitarray 114, as depicted in FIG. 1B.

A combination of rotatable elements and a multi-bounce optical systemreduces the required angular range for torsional elements 402 and 404.As discussed above, and with respect to FIGS. 2A and 2B, each time alight beam is reflected from a torsional element, the angle of thereflected beam is changed by 2Δφ, wherein Δφ is the rotation angle ofthe torsional element. In a multi-bounce optical system, therefore, theangle of the reflected beam is changed by 2Δφ each time the light isreflected from the torsional element. In other words, the impact of arotation, Δφ, of either of element 402 and 404 on the output angle,θ_(Out2), of output beam 106 is multiplied by n (i.e., Δθ_(Out2)=n2Δφ).

FIG. 4B depicts beam-steering system 104 in a first activated state inaccordance with the illustrative embodiment of the present invention.Output beam 106-0 represents output beam 106 when element 404 is in itsquiescent state. In the first activated state, element 404 is rotatedabout rotation axis 412 by −Δφ2. Output beam 106-1 represents outputbeam 106 after rotation from the position of 106-0 within the y-z plane.Output beam 106-1 is rotated by −4Δφ2 (i.e., n2Δφ2, where n=2), whichcorresponds to the extreme negative output angle of beam-steering system104 within the y-z plane of angle cone 108.

FIG. 4C depicts beam-steering system 104 in a second activated state inaccordance with the illustrative embodiment of the present invention.Output beam 106-0 represents output beam 106 when element 404 is in itsquiescent state. In the second activated state, element 404 is rotatedabout rotation axis 412 by +Δφ2. Output beam 106-2 represents outputbeam 106 after rotation from the position of 106-0 within the y-z plane.Output beam 106-2 is rotated by +4Δφ2 (i.e., n2Δφ2, where n=2), whichcorresponds to the extreme positive output angle of beam-steering system104 within the y-z plane of angle cone 108.

The present invention derives several benefits as a result of themagnification of the rotation angle. First, the maximum rotation angleof a torsional element, φ_(Max), to affect a desired angular range foroutput beam 106, θ_(Max), is reduced by a factor of n. Because thepresent invention reduces the requirement on angular range, the designspace for elements 402 and 404 is relaxed. As a result, embodiments ofthe present invention can exhibit:

-   -   i. lower drive voltage requirement; or    -   ii. larger optical beam size; or    -   iii. simpler drive electronics; or    -   iv. lower polarization-dependent loss; or    -   v. faster response; or    -   vi. any combination of i, ii, iii, iv, and v.

Second, because the range of angles required for the torsional elementsis reduced, the speed at which the elements can move from one positionto another is increased.

In some embodiments, the value of θ_(In2) is increased so that thenumber of times that optical path 430 hits elements 402 and 404 isgreater than 2. It should be noted, however, that aberrations on outputbeam 106 typically increase with increasing n.

In some embodiments, at least one of element 402 and 404 is suitable forinducing an optical effect on output beam 106. In these embodiments,method 500 continues with optional operation 507, wherein an opticaleffect, such as phase modulation, spatial modulation, chromaticfiltering, and the like, is induced on output beam 106. In amulti-bounce system, the magnitude of such an induced effect ismultiplied by the number of times that light beam 428 hits the element.For example, in an embodiment wherein one of elements 402 and 404comprises a phase modulator, the phase modulator induces the same amountof modulation each time the optical path 430 hits the element (i.e., theamount of phase modulation is doubled when n=2, tripled when n=3, etc.).Stronger optical effects are enabled, therefore, than might bepractically achievable with only one interaction between an element andthe light beam. It should be noted that multiplication of the inducedeffect must be accounted for in the design of the optical beam-steeringsystem or in a control loop that controls the effect. In someembodiments, aberration correction is employed to ensure that an opticalbeam is incident in the same place each time that it arrives at the sameelement. Such aberration correction is particularly attractive inembodiments wherein an element comprises a spatial light modulator.

FIG. 6 depicts a schematic diagram of details of a one-dimensionalbeam-steering system in accordance with a first alternative embodimentof the present invention. Beam-steering system 600 comprises element402, element 404, and reflective imager 406. Beam-steering system 600receives input beam 102 at a fixed angle and provides output beam 106along any desired angle within a one-dimensional angular cone.

Beam-steering system 600 is analogous to beam-steering system 104, withthe exception that rotation axes 408 and 412 of elements 402 and 404,respectively, are parallel, rather than orthogonal with respect to oneanother. As a result, the maximum angular range for output beam 106,within the y-z plane, is twice that attainable with beam-steering system104.

FIG. 7A depicts a schematic diagram of details of a two-dimensionalbeam-steering system in accordance with a second alternative embodimentof the present invention. Beam-steering system 700 comprises elementarray 706 and reflective imager 406. Beam-steering system 700 issuitable for independently steering each of a plurality of output beamsalong any angle within two-dimensional angular cone 108. Beam-steeringsystem 700 is analogous to two independent instances of system 104,wherein reflective imager 406 and optical axis 416 are common to bothsystems.

Beam-steering system 700 receives input beam 102 at an angle of θ_(In2)with respect to optical axis 416. Beam-steering 700 provides output beam106 at an angle of θ_(Out2) with respect to optical axis 416.

In similar fashion, beam-steering system 700 receives input beam 714 atan angle of θ_(In3) with respect to optical axis 416. Beam-steering 700provides output beam 716 at an angle of θ_(Out3) with respect to opticalaxis 416.

FIG. 7B depicts a schematic diagram of details of element array 706.Element array 706 comprises elements 402, 404, 702, and 704.

Mirror optical axes 410, 414, 710, and 712, of elements 402, 404, 702,and 704 are each parallel to optical axis 416. Elements 402, 404, 702,and 704 form a 2×2 array of elements that is symmetrically arrangedabout optical axis 416, which defines the intersection of the x- andy-axes as shown. Elements 402 and 404 form a first working pair ofelements. Elements 702 and 704 form a second working pair of elements.Each working pair is arranged diagonally within the 2×2 array. Eachelement is separated from the y-axis by a distance equal to d. Further,each element is separated from the x-axis by a distance equal to d1. Insome embodiments, d and d1 are equal. In some embodiments, d and d1 arenot equal. In some embodiments, distance d1 is made as small as possiblein order to reduce aberration. Still further, optical axis 416 andmirror optical axes 410 and 414 are coplanar in first plane P1. Insimilar fashion, optical axis 416 and mirror optical axes 710 and 712are coplanar in second plane P2. In some embodiments, elements 402 and404 are arranged such one of rotation axes 408 and 412 is orthogonal toplane P1 and the other of rotation axes 408 and 412 is coplanar withplane P1 and orthogonal to optical axis 416. In some embodiments,elements 702 and 704 are arranged such one of rotation axes 708 and 412is orthogonal to plane P2 and the other of rotation axes 708 and 412 iscoplanar with plane P2 and orthogonal to optical axis 416.

It should be noted that the number of elements included in element array706 is limited only by the optical system and physical limitations onsize and spacing of the elements themselves. It is desirable thatelements that operate in pairs be symmetrically arranged about opticalaxis 416, however. Further, in order to enable two-dimensionalbeam-steering, it is desirable that the rotation axes of each element ina working pair be arranged orthogonally to one another.

FIG. 8 depicts a method for independently controlling the direction ofeach of a plurality of output beam in two dimensions, in accordance withthe second alternative embodiment of the present invention. Method 800includes the operations of method 300 and continues with operation 801,wherein a value for the angle of input beam 702, relative to opticalaxis 416, is selected. Operation 801 is analogous to operation 302 ofmethod 300.

At operation 802, input beam 714 is received at element 702 andreflected by element 702 as light signal 718 on optical path 720. Byvirtue of the value of θ_(In3), optical path 718 hits each of elements702 and 712 twice.

At operation 803, output beam 716 is provided at element 704. Outputbeam 716 is provided at angle θ_(Out3), with respect to optical axis416. When system 104 is in its quiescent state output angle θ_(Out3) andinput angle θ_(In3) are substantially equal.

At operation 804, a control voltage is applied to element 702 to controlits rotation angle about rotation axis 708.

At operation 805, a control voltage is applied to element 704 to controlits rotation angle about rotation axis 412.

Operations 804 and 805 collectively enable control of the direction ofoutput beam 716 along any angle within two-dimensional angle cone 108.

In some embodiments, method 800 continues with optional operation 806,wherein output beam 106 and output beam 716 are each directed to thesame point in space. In some embodiments, this point in space is thelocation of a single qubit 118-i,j in qubit array 114.

FIGS. 9A and 9B depict schematic diagrams of a side view of a torsionalMEMS element for inducing an optical effect on output beam 106 inaccordance with a third alternative embodiment of the present invention.Element 900 comprises plate 902 and surface 904. Plate 902 is analogousto plate 302, described above and with respect to FIGS. 3A and 3B.

Surface 904 is disposed on plate 902. Surface 904 is a deformable mirrorsuitable for controlling wavefront 912 of output beam 910.

FIG. 9A depicts surface 904 in an unenergized state, in which it is aflat mirror surface. Light beam 906 is characterized by non-planarwavefront 908. Unenergized surface 904 reflects light beam 906 as outputbeam 910-1, which is characterized wavefront 912-1, which issubstantially unchanged from wavefront 908.

FIG. 9B depicts element 900 in an energized state, wherein its surfacehas been deformed to provide wavefront correction for light beam 906.Light beam 906 is reflected by energized surface 904 as output beam910-2. By virtue of the wavefront correction induced by energizedsurface 904, output beam 910-2 is characterized by substantially planarwavefront 912-2.

It should be noted that element 900 is only one example of an elementthat induces an optical effect on a reflected light beam. One skilled inthe art would recognize that alternative embodiments of the presentinvention can be envisioned wherein surface 904 comprises one or more ofan adaptive optic element, deformable mirror, spatial filter, phasemodulator, spatial light modulator, shutter, chromatic filter,polarization filter, polarization phase filter, polarizer, and the like.It should also be noted that surface 904 can an active surface, such asthat depicted in FIGS. 9A and 9B, or a passive surface that remainsphysically unchanged during operation.

It is to be understood that the disclosure teaches just one example ofthe illustrative embodiment and that many variations of the inventioncan easily be devised by those skilled in the art after reading thisdisclosure and that the scope of the present invention is to bedetermined by the following claims.

1. An apparatus comprising: an optical system, wherein the opticalsystem receives a first beam at a first input angle, θ_(In1), withrespect to an optical axis, and wherein the optical system directs thefirst beam at a first output angle, θ_(Out1), with respect to theoptical axis, and further wherein the optical system comprises; a firstelement whose angular position about a first rotation axis iscontrollable; a second element whose angular position about a secondrotation axis is controllable; and a reflective imager; wherein a changein the angular position of the first element about the first rotationaxis by Δθ1 results in a change in θ_(Out1) that is greater than|2xΔθ1|; and wherein a change in the angular position of the secondelement about the second rotation axis by Δθ2 results in a change inθ_(Out1) that is greater than |2xΔφ2|.
 2. The apparatus of claim 1:wherein the first element and the second element are located in a firstplane that is orthogonal to the optical axis; wherein the first plane islocated at substantially twice the focal length, f1, of the reflectiveimager; and wherein the first element, reflective imager, and secondelement collectively define a first optical path in which the first beamis incident on each of the first element and the second element n times,where n>1.
 3. The apparatus of claim 2: wherein the change in theangular position of the first element about the first rotation axis byΔφ1 results in a change in θ_(Out1) that is substantially equal to|2nΔφ1];and wherein the change in the angular position of the secondelement about the second rotation axis by Δφ2 results in a change inθ_(Out1) that is substantially equal to |2nΔφ2].
 4. The apparatus ofclaim 2 wherein the optical system further comprises: a third elementwhose angular position about a third rotation axis is controllable; anda fourth element whose angular position about a fourth rotation axis iscontrollable; wherein the optical system receives a second beam at asecond input angle, θ_(In2), with respect to the optical axis, andwherein the optical system directs the second beam at a second outputangle, θ_(Out2), with respect to the optical axis; wherein the thirdelement, reflective imager, and fourth element collectively define asecond optical path in which the second beam is incident on each of thethird element and the fourth element m times, where m>1; wherein achange in the angular position of the third element about the thirdrotation axis by Δφ3 results in a change in θ_(Out2) that issubstantially equal to |2mΔφ3];and wherein a change in the angularposition of the fourth element about the fourth rotation axis by Δφ4results in a change in θ_(Out2) that is substantially equal to |2mΔφ4|.5. The apparatus of claim 4 wherein m and n are equal.
 6. The apparatusof claim 1 wherein the first rotation axis and second rotation axis areorthogonal.
 7. The apparatus of claim 1 wherein the each of the firstelement and the second element is a mirror.
 8. The apparatus of claim 1wherein at least one of the first element and the second elementcomprises a mirror having a surface that is controllably deformable. 9.The apparatus of claim 1 wherein at least one of the first element andthe second element comprises a spatial light modulator.
 10. Theapparatus of claim 1 wherein at least one of the first element and thesecond element comprises a chromatic filter.
 11. An optical systemcomprising: a first element having a first optical axis, wherein thefirst element is controllably rotatable about a first rotation axis thatis orthogonal to the first optical axis, and wherein the first elementreceives a first optical signal at an input angle, θ_(In), with respectto the first optical axis; a second element having a second opticalaxis, wherein the second element is controllably rotatable about asecond rotation axis that is orthogonal to the second optical axis, andwherein the second element provides the first optical signal at anoutput angle, θ_(Out), with respect to the second optical axis; and areflective imager having a focal length, f1, and a third optical axis,wherein the first optical axis, second optical axis, and third opticalaxis are substantially parallel and substantially coplanar, and whereineach of the first optical axis and second optical axis are separatedfrom the third optical axis by a distance, d; wherein the first elementand the second element are substantially coplanar in a first plane thatis substantially orthogonal to the third optical axis, and wherein thefirst plane is located at a distance substantially equal to 2f1 from thereflective imager; wherein a first optical path between the first pathand the second path includes the first element, second element andreflective imager, wherein the first optical signal is incident on eachof the first element and second element n times, wherein n>1; wherein arotation of the first element about the first rotation axis by a firstangle, φ1, results in a change in θ_(Out) that is greater than |2φ1|;and wherein a rotation of the second element about the second rotationaxis by a second angle, φ2, results in a change in θ_(Out) that isgreater than |2φ2|.
 12. The optical system of claim 11 wherein the firstrotation axis and the second rotation axis are orthogonal.
 13. Theoptical system of claim 11 wherein the first rotation axis and thesecond rotation axis are parallel.
 14. The optical system of claim 11wherein each of the first element and the second element comprises amirror.
 15. The optical system of claim 11 wherein at least one of thefirst element and the second element comprises a mirror having a surfacethat is controllably deformable.
 16. The optical system of claim 11wherein at least one of the first element and the second elementcomprises a spatial light modulator.
 17. A method comprising: providingan optical system having an optical axis, wherein the optical systemcomprises a first element, a second element, and a reflective imager,wherein the first element is controllably rotatable about a firstrotation axis, and wherein the second element is controllably rotatableabout a second rotation axis; receiving a first input beam at theoptical system, wherein the first input beam is received at an angle,θ_(In1), relative to the optical axis; providing a first output beamfrom the optical system, wherein the first output beam is provided at anangle, θ_(Out1), relative to the optical axis; selecting a first valuefor θ_(In1), wherein the first value enables a change in the rotationangle, Δφ1, of the first element about the first rotation axis to inducea change in θ_(Out1) that is greater than |2Δφ1|, and wherein the firstvalue enables a change in the rotation angle, Δφ2, of the second elementabout the second rotation axis to induce a change in θ_(Out1) that isgreater than |2Δφ2|; controlling the angular position of a first elementabout a first rotation axis; and controlling the angular position of asecond element about a second rotation axis.
 18. The method of claim 17further comprising selecting the first value for θ_(In1) such that thefirst value enables a first optical path comprising the first element,the second element, and the reflective imager, wherein the first opticalpath is incident on each of the first element and second element ntimes, where n>1; wherein a change in the angular position of the firstelement about the first rotation axis by Δφ1 results in a change inθ_(Out1) by an amount substantially equal to |2nΔφ1]; and wherein thechange in the angular position of the second element about the secondrotation axis by Δφ1 results in a change in θ_(Out1) by an amountsubstantially equal to |2nΔφ2].
 19. The method of claim 18 furthercomprising: receiving a second input beam at the optical system, whereinthe second input beam is received at a second input angle, θ_(In2),relative to the optical axis; providing a second output beam from theoptical system, wherein the second output beam is provided at an angle,θ_(Out2), relative to the optical axis; selecting a second value forθ_(In2) such that the second value enables a second optical pathcomprising a third element, a fourth element, and the reflective imager,wherein the second optical path is incident on each of the third elementand fourth element m times, where m>1, and wherein the second valueenables a change in the rotation angle, Δφ3, of the third element aboutthe third rotation axis to induce a change in θ_(Out2) that is greaterthan |2Δφ3|, and wherein the second value enables a change in therotation angle, Δφ4, of the fourth element about the fourth rotationaxis to induce a change in θ_(Out2) that is greater than |2Δφ4|;controlling the angular position of the third element about a thirdrotation axis; and controlling the angular position of the fourthelement about a fourth rotation axis.
 20. The method of claim 19 furthercomprising: directing the first output beam to a first position; anddirecting the second output beam to the first position.
 21. The methodof claim 17 further comprising controlling the wavefront of the firstoutput beam.
 22. The method of claim 17 further comprising controllingthe phase of the first output beam.
 23. The method of claim 17 furthercomprising controlling the polarization of the first output beam. 24.The method of claim 17 further comprising providing one of the firstelement and the second element as a spatial modulator.
 25. The method ofclaim 17 further comprising controlling the wavelength content of thefirst output beam.